There are a variety of representations of three dimensional sound including channel-based approaches like 22.2, object based approaches and sound field oriented approaches like Higher Order Ambisonics (HOA). In general, each representation offers its special advantages, be it at recording, modification or rendering. For instance, rendering of an HOA representation offers the advantage over channel based methods of being independent of a specific loudspeaker set-up. This flexibility, however, is at the expense of a rendering process which is required for the playback of the HOA representation on a particular loudspeaker set-up. Regarding the modification of three dimensional sound, object-based approaches allow a very simple selective manipulation of individual sound objects, which may comprise changes of object positions or the complete exchange of sound objects by others. Such modifications are very complicated to be accomplished with channel-based or HOA-based sound field representations.
HOA is based on the idea of equivalently representing the sound pressure in a sound source-free listening area by a composition of contributions from general plane waves from all possible directions of incidence. Evaluating the contributions of all general plane waves to the sound pressure in the centre of the listening area, i.e. the coordinate origin of the used system, provides a time and direction dependent function, which is then for each time instant expanded into a series of Spherical Harmonics functions. The weights of the expansion, regarded as functions over time, are referred to as HOA coefficient sequences, which constitute the actual HOA representation. The HOA coefficient sequences are conventional time domain signals with the specialty of having different value ranges among themselves. In general, the series of Spherical Harmonics functions comprises an infinite number of summands, whose knowledge theoretically allows a perfect reconstruction of the represented sound field. In practice, for arriving at a manageable finite amount of signals, that series is truncated, resulting in a representation of a certain order N, which determines the number O of summands for the expansion given by O=(N+1)2. The truncation affects the spatial resolution of the HOA representation, which obviously improves with a growing order N. Typical HOA representations using order N=4 consist of O=25 HOA coefficient sequences.